The only dies currently on the market that don't fit in the Big Shot are the very widest ones in some sets of the Grand Nesties, and some of the Sizzix Bigz Pro dies (which were made for the Big Shot Pro which is 12" wide) - although really, if you have a Cricut you can probably cut almost any of these larger shapes very easily. And probably some AccuQuilt dies but you're probably not needing to cut fabric And now that the Craftwell eBosser has been released I understand they have some wider embossing folders.
The only machine I know of that can do absolutely everything right now is the Big Shot Pro, but it has a hefty price tag. Also the AccuCut has 12" wide cutting, but I don't know if it can do the fat Sizzix dies or not, I'm not very familiar with them; these are also more expensive, of course. All other machines I've seen have some limitation or other.
I'm not very interested in the Grand Nesties, so I have a Big Shot, tons of dies from almost every company you can think of, and I adore it